Worked solution · Exam FM
This Exam FM sample reference tests Coupon Bond Price Anchored by a Zero Bond. The zero price fixes the maturity discount factor at 0.64. A coupon rate equal to half the yield contributes half of the 0.36 discount margin, so price is 0.82 times face. Face is therefore 780.49, choice A.
Independent solution
Setup
Normalize the zero-coupon price to obtain the common n-year discount factor.
Model
Let F be the second face amount. Its annual coupon is one-half of Fi.
Compute
Use the identity that i times a-angle-n equals one minus the maturity discount.
Answer
The face amount is 780.49, which rounds to choice A.
Test the method on unseen problems
30 original bonds problems with complete solutions and wrong-choice analysis. Written for Exam FM, not copied from the SOA set. One-time $19 PDF.
Error diagnosis
These notes identify the calculation error associated with each wrong letter when that error is reproducible.
Original practice · fully worked
A 1,000-face zero-coupon bond and a 900-face coupon bond share one maturity and annual yield. The coupon bond's annual coupon rate is half the yield, and both bonds sell for the same price P. Determine P.
Writing the common maturity discount as P/1000 makes the coupon-bond price equation linear in P. Solving gives P = 818.18, choice C.
Setup
The zero price determines the common discount factor.
Model
Price the 900-face bond using coupon rate one-half of yield.
Compute
Insert the zero-bond expression and solve.
Answer
Both bonds sell for 818.18, choice C.
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